{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5e5ad7d3",
   "metadata": {},
   "source": [
    "$作业背景：有两种广告banner色调，通过ABtest做择优选择$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83921e02",
   "metadata": {},
   "source": [
    "步骤：确定一二类指标；选择统计量；设置埋点；设定H0和H1；计算最小样本量（之后需检验实验样本量是否满足最小样本量）；选择检验策略，计算P值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "6a036cca",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "from scipy import stats # 统计函数\n",
    "plt.rcParams['font.family']='Kaiti' #中文字体为楷体\n",
    "plt.rcParams['axes.unicode_minus']=False #让中文字体/负号可显示"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "f4d3a119",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>timestamp</th>\n",
       "      <th>group</th>\n",
       "      <th>landing_page</th>\n",
       "      <th>converted</th>\n",
       "      <th>date</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>851104</td>\n",
       "      <td>2017-01-21 22:11:48.556739</td>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>0</td>\n",
       "      <td>2017-01-21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>804228</td>\n",
       "      <td>2017-01-12 08:01:45.159739</td>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>0</td>\n",
       "      <td>2017-01-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>661590</td>\n",
       "      <td>2017-01-11 16:55:06.154213</td>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>0</td>\n",
       "      <td>2017-01-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>853541</td>\n",
       "      <td>2017-01-08 18:28:03.143765</td>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>0</td>\n",
       "      <td>2017-01-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>864975</td>\n",
       "      <td>2017-01-21 01:52:26.210827</td>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>1</td>\n",
       "      <td>2017-01-21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>294473</th>\n",
       "      <td>751197</td>\n",
       "      <td>2017-01-03 22:28:38.630509</td>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>0</td>\n",
       "      <td>2017-01-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>294474</th>\n",
       "      <td>945152</td>\n",
       "      <td>2017-01-12 00:51:57.078372</td>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>0</td>\n",
       "      <td>2017-01-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>294475</th>\n",
       "      <td>734608</td>\n",
       "      <td>2017-01-22 11:45:03.439544</td>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>0</td>\n",
       "      <td>2017-01-22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>294476</th>\n",
       "      <td>697314</td>\n",
       "      <td>2017-01-15 01:20:28.957438</td>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>0</td>\n",
       "      <td>2017-01-15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>294477</th>\n",
       "      <td>715931</td>\n",
       "      <td>2017-01-16 12:40:24.467417</td>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>0</td>\n",
       "      <td>2017-01-16</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>294478 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        user_id                   timestamp      group landing_page  \\\n",
       "0        851104  2017-01-21 22:11:48.556739    control     old_page   \n",
       "1        804228  2017-01-12 08:01:45.159739    control     old_page   \n",
       "2        661590  2017-01-11 16:55:06.154213  treatment     new_page   \n",
       "3        853541  2017-01-08 18:28:03.143765  treatment     new_page   \n",
       "4        864975  2017-01-21 01:52:26.210827    control     old_page   \n",
       "...         ...                         ...        ...          ...   \n",
       "294473   751197  2017-01-03 22:28:38.630509    control     old_page   \n",
       "294474   945152  2017-01-12 00:51:57.078372    control     old_page   \n",
       "294475   734608  2017-01-22 11:45:03.439544    control     old_page   \n",
       "294476   697314  2017-01-15 01:20:28.957438    control     old_page   \n",
       "294477   715931  2017-01-16 12:40:24.467417  treatment     new_page   \n",
       "\n",
       "        converted        date  \n",
       "0               0  2017-01-21  \n",
       "1               0  2017-01-12  \n",
       "2               0  2017-01-11  \n",
       "3               0  2017-01-08  \n",
       "4               1  2017-01-21  \n",
       "...           ...         ...  \n",
       "294473          0  2017-01-03  \n",
       "294474          0  2017-01-12  \n",
       "294475          0  2017-01-22  \n",
       "294476          0  2017-01-15  \n",
       "294477          0  2017-01-16  \n",
       "\n",
       "[294478 rows x 6 columns]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('./ab_data.csv')\n",
    "data['date']=data.timestamp.str[:10] #转换时间戳为字符，提取前10个字符\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "738de664",
   "metadata": {},
   "source": [
    "### 确定检验指标"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfe1598a",
   "metadata": {},
   "source": [
    "$一类:人均在线时长(下降量低于一定范围)；\n",
    "二类：广告点击率（提高）$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c03b1c18",
   "metadata": {},
   "source": [
    "### 选择统计量"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32a75c96",
   "metadata": {},
   "source": [
    "$均值差：两个方案的人均在线时长之差；比例差：两个方案的广告点击率之差$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "441c5b32",
   "metadata": {},
   "source": [
    "### 设置埋点:what where who how "
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "3867e13a",
   "metadata": {},
   "source": [
    "$广告曝光、点击，在线时长$\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb78bc06",
   "metadata": {},
   "source": [
    "### 设定H0和H1"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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nleVrbX2P6/U5dxz+ujpJQb7Vgrbf2yIXRPL56rH8wKf1f9ta2IYcfxNlm8p7DiTf8nTARUe4YJWL/PI/QpUIcHWuLot9H96+f39+fNhjk1Tndu3G6PoLhhjPPr53yHBY1d4YwPGVz6unz7IX+iHm7xwr07EhYHBblHDKfFkbYCtOKvvfUui0tZ2nlccYfZ28P0xg82TZTjYYQO2EAQcXsnZ+48skldObhHoObgbQXwoO+tttJztxKNstV3YK+TyyhMCrfdey2P3BSEc7gyLLAp2HhUrZ1/eAyQMJ7OFyHyCzBWZKvtRn4TOJAIqN5Q5IxQJjtrwkTSBC8jtjRvjealkQx9WCSfFA7jDpSubZAlJtb2wbMv8NZakm1OYiNJKfCtJKMNn17JKKQe6/ygZpTEbxLIEFHn8N2T0VdUoxoO9HxQf4vI1PB23D7MDFi40oE5C0sowuJGyllYsTO862bZ87dxl68yzuYMXExUkvaqtERjpuVQjee04+V58oXczdA77jqiZGNfbdywsQfzFeWu7hCvzSg1nmMV6PE/J3CWzA1DqinSy9gYVj/sT6OBPZlsuBPc5SnhYJcqdzNei9fZPFlNsB5X9y0o6HZpJ4WzD4vUnHaqETZOcqObYp9qhlMfvXyxImwI5cCybaghyVUsieyn8xbdf9ttVWjmBg3xGEkvw9LKfkhh4qLeRCkDzut5QTY2WNwCd5HBuJL0kWtv6D3t4ELsecKnUT6qerZeFDawXlzoVkXTGZnfrLOnRsXc6h/LnyOxG2yOooCY3LCGR5h3eXJCZ/Zuy7ZhORoG8XjKvS3mEgRX1qkw0wRLxo4YUe/vh52/hgSSN84aBfYJQxy/HqEoictSvwcy4aQGYhFxoOjpdiKs4d9ptlq7Pn8SJGxnqep+olRNHeuQ0M6IhFe3xZEH+2303K+KKX+je3LUksWWZzuV6Xy1nuyuZ4amGtW2j3TZvn6yJLZ0IsceJiW3f/kVtYani5Y5lk9rNt+u6Xua754wQ2wtEOBDhUDqCybECc6pG3NmvjtPuQKw8UnTTN4Nl8rPC+lMXR2yHJSYsyFre/JWeFsnxOcVXHCxIhSKV1fjpBaQ1nozMxxrpjfFQ2tLGGnVZw5PAOod17AlBqoyEKob8cOGZsnduQtd15osgXQCcNvnYiyee9OuWxYtLBRL6KW9Kjh1Mi4FeThh1PZs8msPGCMk9cK9kX4DLwN7mrEwnJ2Idru0eoxxnYluh4zivHBnbp+WXSrTE54qa5SEavbdyNZ746PiA2dC7egU3vt8WmtZWNgY09QsPZx/zzvd7NcfVlj0CactWmla32YezneCWVIWuei9Fkz3/C+QpnIWvehV99TJ59ETlO1YWiTodJHjnf3smQC1mM21ZeyF3/ah2Ng9DZzq11rTv3K3z2tZbnod1+tK9jrUUCm6DIDioH4EClE75ysXIUE3LFB2M0m4NM29ZfL4tZT1D1PlxHA1iJkU5+3fWwbcDV2/hpAMcBXbeLjtMvBmA1chAMXCJW3XLCZCAP67lk7ZSuhKs+KknaXWCjAaktsnqkh7t4Z7pCl4upOgAX+yjnkIei/yPk1Qbho8Z+0v6pfjhLMkgIgKeEf7otXRM8g2O0bztpApNAAMNDedUtbmSe5FfbN2U8G3d8bEkZ16KdyTW7ccxelrPIIA+vVWM2wFgdq8t4+wp/d8PaBQ+pGv0tPmmchIkcx4FPzy+TD6FYFAN9tvaS874tvzw+wKeOIrAJd5A+vRNwTj7WxGHYZHt2MrsWxu0egpUzxyEDGHytutuWO5JgF8dr6VihhO8/ubLcyQDJxLwAkrz1N3cv8uc+mi3I2+DelAwHslz2DrCcyhh7d6L81jYcVTlNnN5QPRbNMmZ8NjdyV4UfI7B58G514GF5M8G21rjpIGrPbT0C+e2EcA2Tv0lSmUYxUXXWIMGJrfelYwiICCC6L62jXm+QmvO2aanaBh3olLNnsczKwEIfVQdt+xmOTHKCJJFEjCYSELuqj9yiv4V+tj3UFsAx6wRxJZ9JhtxuzoFtBZ+gYrprMCSwLf6lVtmH6rvDZbm4B92zv5j2q9tsvTEV1teFTHG8PbctA5v767XvHvdsXPnY7SpvhoBd4m+4IzOa0DyQDNmLt1R7D3yJLnVWNy5X8MQNXaXbgq1IlhjuwAgdJkyyfZOCRieoDF+Id2gkW33JF1wX3HIt/bgdv1lWiPDR8QE+NYo7AND5BabAIu6n+SA8XCxL3JI/aV9IeOQlAo39nL56hyL+4v+l7Xrl+8dh23476Av62ram/EArWOLc38bte7kQtheK2szqxiyps9laO5+bDtR+2+/8rsqubfexN5KETW1TT8zqqhUO3/g5AntdecI9Z1VkgJZrc9wsnUy07u2ESEgwWXoDcLs1sQY2r7FDQJN+Ts0rlRAgegMkrt2JxChJU09E1X58A0PEZsyLbLBMV8KprfBwDtb2pbWAeRkCSG51VV5npbzssUuQM8rASmyB7WEgh7ybjAfMI8HZVDW9xio+IBHrBx9MWbCwXnI2qypqJ/lHOgIHnfQyXGkL+swEOkuSUnWLoT4kEjPelwsIYZ19aITQA3HSav0ZeszgPV0WQT41inpik+6YV0n7G3bitdt1De3PKgWZwkOkdY2BX6Oebautno44dkTZ1E6INRjD8pv8Es2r7Epy4Efw6xhDUD40D1+Rh/fQ9rfFB9gh4LKSzQPm5he4RtwSpiCsklswWcdQTfsD7vUFkWl8ZhM2mlxvPm4SPuHHFugaY1Nc/nRJt/Zxq78ft8Y9986iz8Ive4Xd4yB1bYzS4nLnSS+EB+WkgrWf81Crthk2YrIBnMP+Yg6Afvac3W719tuU8X8zWeK2XinZo/Z+jMCOYMyGkvUtWC8mT0C2xHDUTj5nnQUOlM8euFUMCHu1hgCxMkisKClAqUOafb09ld7AoFdkNbnEPkhmWjsMQmUHTNwu5YuTOgLuyq8KGpXoERw5C3ucLyDXfuBUOBCsqz70vLuBAJbk3lTXNAiiUFwloO0ot+gzXJNtbGdaNptor8TfFBDU0lhYwcrgu2bf3P5826jTs6/adiJNPF0Wk4fa8Hb/q3IQ9FObXQKLvpUAAgE7qQkZMcfDJjCtbJp8YS4OJb8wxEh7Ubn8cSny5PFbybDYNbrOnSmMN13igT7KdnL7OD/4rQDq+Y/op37xyPig+MlFXJR7OIYV+LihMord0Valo1ZJ7wOvx6MsmZI1622WXmv6G+hP7BMuMra1Ee5gVGvwY8KoShTJ/KsPRcL28Gtra5xL4hYJALlzVd15FDxW3qdc4OujMD6qPuzHy5wAEj0q+XV8VLha3LsXz4jlsV1dQpeWwWHcQ7/aJ7BfupJtM9pcknh4K4S84xsJv7LeGKIjz74ZgS3T9qsECURp5reLmn0QAw6FwSJr87KRxGDh1kK3rfpEvN0Xr1bqc8fv6+BQb4Ie/mDyJIgODhwQ1NN+GJyyjXZtMHG2ZQIM5Nr0H2wVe8ZgwuCCPDrJIAvj/eIWpOoaa2tdJzqjv1BFFvVLmZvcpkbP1S+CUdVHVarcRZ3TZbmECSpjWRZc2UtBy2ID+8Zjxgad9ZeFvk53SgSG+qEfY0OnrXBILliQLTaBzupQVx3ZS8qGGCBZpWTPXvlG18ETtk1ZCFW/Bxk+Jm8V8HxwwzF1x+QfgDzqU2MLzPOyGoiov7hd3EyChtgYAtrilpYiFBdIaH2dwIaHWGzcLfSKy5qQLVvDDrYNvX97fFAycl4uKWsdycNcZrTwXcQaOFMYL9flAr9NFwLhgzw3GUvx9WYgK/gNzwD4a9DgEJLaTUuuhMhgToTfyhya15vmSuUWZEe/3d8wb0gsqQioEDzjc2Xr+Y5TbreKvcDLjIu6DchoIK2LDPYzRm3Mi+NNZXNlQH3garvKMSG2UXIRyO0v63Ay/cYP/enP9ufcIdP6cd7fh5fVb9/2WxHYGGQdItRcke8o0yBsiWudZYXxsiPV69/2ZmX3mcmplQZjuwbPXr2NBoTTZpj75MGlPPDjwMj7qOW/6qd+qEinbVTLvxgAzkD2J/VcNWyhfmXXdqLO9TDIcxXg0+oXagFjd5LP7dot+HAIYDvqa1tJvzYQagmxVn5i3cGx1TfXxbki4JnJIU8UuBvRX9KRWzVbsI8jlymVsl7xlnxc3hPX/GqgxyScbAB86/PYh21RzsMPuqOsyoMJ7oh4U7SR/SvKleNKvS+yjGSPssYJSS5oMJnVLgod49Kc5OeFLUa+75VPKPX8MsmimML+BQ5+3NY6agifhOO0hxnO6S/6rxqPdbM9tLzGPnvRMMIoEybPx2y7xTbkQma9unvmvfvY1oddo1oY/1EfnINP2GUustbaEkKZz8LXJpN9Kphsl6KoIa+SlCjvYMFfw7wxJMIlAY0xJrUtF+Eaf9C9V74+hrLlb8/OKmtHYWDYOV12YvesHSU7bc4h8YAY5b/BQCoA57K+aWpp24pz7Jpeto2wXdmwf94fK6G8xh87ZpqWHnrg5whsJKLp6XIZvM3T0YJ3XE4Qrlxr+OvbMm79utLx+y2hzlmq3Nv6gMhl45YOBGfi6QXq8DSpE7iKzErRURl4i1M6gfcHcSiPAVhFGsivt1DsLau07qioooPQ6S+d6+ldy6239PQCYDv+2mbSb71vYCm+XD4M1A3GwC7YGHpDVp9kIPi2v16Ag0zVORk7YQ26T1Jt25LJDWvOw5q3fFHWtW9tW9UR+imy+VaxnWXk9HQGFhN4It4Tmdg0zUQiYNZ4YqmSvEsyZipT2yHrK6SjtGnQQv3yGnRxy5iLm3NaR1r7EvzDrj+PKCVf8Pru+WWSScdWr1w2Q98OKnvlP6lu9IHWrqbp7u31rv9InKh9SBo8Mj5Iex2/DARTY25/jTVspjhDvnAgfknRSxvEej6eBW71TpF5TZjXOoRb8zlurCV3ZL6QBzOLMaEKZQFgKxsX2m3fD2JdT98c55wuBz6Z5aq3ClJZkddQFng1GeW6Jcjm66SlwUHM+IRf2OSTlvc2IBMupKoy2p7poypiCDcJbIvNQ47AQXrEFZ1irRYGGY7bX5vB9QaKLfu47WLw1M4IJx06YSlb/aLp+OAa3o0XQ05JWEFW6kHXnwQxOOoJFZIcMUG1gS4H2DpwaaCscVKi4E0JkDb/Qi9LCNB2T9dcu9pKtpurJ7cG29s8kKfU14yBgsDKRZv/OjF3nZqWzQ8UQgP0W8uO47BNJKnJt1IGBm2EX8nIFAeQnWzHG9q2uvaw98pW3cRdjB/baCrYa9ttBwfRnhKV7JOKiaRSk96xj1ZX9O2IhZ7ib9Ff247N4Jdt9ccuCFhtWxA9bWfCf3t2wPGmj6Rd1L+ON6XqkNOORSkB7IC396s6FP21F4jQuSdnJVHcVZs48tssnvjI1Jgu468fvzM5dy/se7f/VdYkCxTS46UO5VzUXxJR2i/5Wg262kreoICLu/I3XvyVMkDE2Ifn8/Yioj0P33PEQdPmt1wWMFrLHLLLpqa/idjs6+TXwVHUjTElJN/6GaTuhZS2hvfZDoHIfQ6LodEH/L5VBvYB+rVN3rxMZV0sGaYmNHWxsC9XvfU06xZ84MFIpou3CUhvxdX5Hd0Xk1EZMKXVOOirYNDpGwEiZL7TGyHCusnw8uiIYxngOnIjiFYjZxS40HdVRTTQW/F2MkJ5e6wjTf9qFHLWFxf9huKZAvO1wjifL6pER8if9c16yjtIRxMAWszYTAZV6KtjR275ycQj60jj7b/ctplMspDxtLZT9tuzb6urabvC3i1bCJV2IEMtm5zGOc22ew20x/Jt0oiF+jpun9oq7hjaEpsMYVN72A5MjCgwGvSR9G7GRJJVoeqVM917dsCx74sPSXH1m9KvDSw6bgO5ruwGfBRnS/Ruxt6Di6SGtFd9iCwFGa2ziiMdqmys3BUqp0fEIOiffM1ZQqBjw4Jjtkfne3EC1SOO1ZwVhsCo6eMAACAASURBVHW8oLb4ok75Cz2EMPbJellnbS9hUYzFtTrmPDKz1vbNa/hS+ZENO/Oh6SltQl5mYFtsHnKkn2UqX5GVlhjgNqZmm/wM1Tm8UuIhAleNxltEaw9F4Dye5Ay3dDpXsSg7uljDZI1JqwmiafLCeRG6F0Di8SrzFB78yS+6d8vYQWm3q0jT61dkauS26OqAzkEN5a1etordVpmdyUDPVbLa+s12kmem7/CABT66kLCRruogDX30tTThlikmkkaCdACBeq2cFM8BrZkku0QPdUz75rZlrX/PvtCthhjY23Z6ZRsE4BN1o0AGD+E4Nm/a6hyI8hndi3LAfp9PSlPQX+zhq9H2oXb09AImdgyabe0D/iuv9uvEHsQnrVPJqz70BfFBzar49WyeSqZXzvXWNlvMan+OzyeUSZVYJvuRytNslFnFellSKD6hQ7MkQlls8jf1LYx/OydEbMZjA77t4xjrjvRt7+6IbjWWDTzhgHkNlpMl9+vMHAUWvk4zLYQyzYdWnI9WDG2ImODUK4SAvL3YUhR+yM6PZWAz4BocTfDdf+xOh5s1rTqdHezHbGtAlEwQvu0cCI7cwonr8pQEQA6tlHCtg5LuZwVjNi4t2M+Hiy0EH/d2l15MpIsMlSE2gbp14Jeza8FJgq7GWVNe9S6kNDvIlPVIGvDqkgjTFjZTHfQd1jwXF0piJ/NKk+DH5ZOpLRZpqUHoA0FqzXdny0mj5fgKmfWzPG0d17xBtfq3kNNgBd1t+aKsOdG1Ld42MVPWlAmbkKXysVwM2Oz5IlFsJeozsAF8S8YS5JnN0GjdNFZ69ZqlGvV4zhrjYlYypMVFf7qAUqhU1vX4pHVkzIVs/ZfFBwOf4tezhS3rbHt+XhwD7hZUjWUjQieFDDEzd8QaMdDHmg7anu239i3s42t84ldx3ffa2Bid78WJRpfqQIFldQ67sW1nSQkK7P5F/BzEg01tm/hU22rFhqpj5UdF99oGCWyBy2t3rNEf4aT3aDefgY23h6P8vQyIPS63NrUOSH3IQEsGJRLY7Msoi4FW7TsZ2S1ajwKTtoPBk4UKp0aBayY4afsa9FcGJ+QQzCpZvLY2L7LXV9YkX3RvE8U3BNj+ZHuExfzSgMq2dSfV/txar6oS/MXomslruUSnp9MW206XhW0Hds2ExL5/udKv2o3LCOJ6Poy5QPY7GfGocyaCI3FyV5gMI3nQNqYqg1Q4D5ClzGCzXEmOy8UKEn+9clnAJWTpwi1Oc3BiM+qC2NOp0LFdz3+klWm/SF1uLR+qQa6aUHTUqA+3fWJ8Rju352ML8bglknXLWf/Vtwls0qF6d3JTN/ma45dqq14GvzNeRDOtC39s1XWOAMtBzG/kd5rZfQhjdsW3t7SPi9ja31b0gB+N5qtcZoDXFll3lP2xDOw6QmoUWZODW4SyvV7VKZHWpu6u7zQ5cUjlFlK14S0JUi8uN6i0TYPAxhj0gWNhP91O2Ro8QtYlrIeNOMf6K4MYAxACJFxGfdcyr0EZ2xoNTgScmQudHBxHQUGIZf2GCSmvT/ZqQKpf/dZqM8LiUQS2lSIf6S5TgS01i5zrKEFMdoZO8oogewHm3Y42rRSb034AuSofC42FNaupWZRL481m8W3H8Cf3Tk+6TY7sk62nGIT2HVJZFJYd42sqe/ZVPdTUw4FU1rmDEkvIi+brtY2SPa3iRigs/tweD3cP1gWJLUhW9iPjA/A0v+orK/HNVLGb8F254Cn8KNkK40Pe1R0vlNJa6zCX4ZOy5TlrNvncb2stK0Fg+kt8sHOHDiZ+xQv+5GuOLwzHS4gVclHny5BxqGS3u1aWP4un36ZUBf7u0grb9q5tjNF+/71mw2eaHcOpvDVO6oe9+Q2y+HObjF/rf475eqIeepwE1sDpGVsHUbMY3VTsbOb21taSdBrYerjIzsWPMGQn67+aZbWb5KyFk8rta2cS09vInclPgqpkdMMHIsIVdM4sIShEzFcGMQZgIdT4yhv2qKp01Yft3fJmneaYkNrmTVBwFv5DPrWZe/EhF0UzF1QgMT0c185D7tlyKJ9/9cIEk20DZH7oDDrnzGtqJ/kejsMmKF//Nl1kcXQLOK+W9Xws3BaNk11RH2VBwh0bSdAPWUq8GiysVetPwlFg4J/HyehpZ6mjX8yrx6BOOj2fAETJT+v6ejpOXrBJ7FPkazN8sFeBlSHY5fFIgr8iPgCr+lf9ZM0GdcW4r74rXwsLFz32a3ytr9Tjw9/fKMsdOkB+EPCTfE5axkztCJpF7b9/ujtPjD7yYWFVPfLYEh92RNFa8GcfR9uOT/y0IXcD88NGeyhWMWGlS3sQd93lINZX8CW0SneNF1EvLOnDl7jUdluWxrl67z9IAivYVcRPb4MFXO2i9nKN4SrsxgFGg2K1nbUCadG2DqrifXNRfnzyTcr4xHPQSdJjSodU1k5u2nITMNLn/mRCN2mAbmDShkwWoBJqJsBUVWyrZhsDvJ2Ui4yYM2mbRtrNCoOCjATs0oTkXE23jY2OrAVD6BcnCJvNLLcv6f2Y/dfZhPIibxhH9brcFPxkzaTJxJXrd+XiKr9b1Y4/THiwWbRv+/7VR2dgvay41SdaAphiIlu/aBz5esAImSYhk4XvxFhUewDw8siklJX+ZPyP3WtEYKFjNS4gGwwFwXC8JsM4bjNDeizjF16+/2nxAbp7v6rjdpIizcG+NczoqveBmTg+2nETx7r/QBPabH536wDfEd2xnWztKBTXQ49kk0xyKR3wEf/H6//acVrW2bI3M7/keXhtnNU9r8Xsunzez3pj7KRf+XSuibu5hplDEWMcIlrEIC0nfiTAQ95eFrfo7SE7v01gC+Iar176tj6nASGOgVu61ehxTdQOMrfY1oNCWsPXVazDjiZMJ9sVbvmv6YBAIxOW3DqsHt6o9vXqrDiO240ig3y6tQ1KWA+HK/MQBJBhcH+z3iETkQKgBhivThqARaxMD43gFU+47aZZLDvBLvZiJvqBJVvTJtQJADr4ZGSqPchf3DLE17P8zEZsF3Y9L1dzoaXBV4MVZBz/hgsW044Qj3Cbv3AvxwfN8pochBF0IWMmS9G+eR8YoW5h2+rTk9G2G4Ku0Udx6b2WBoIEHm9jRcTNvaDTzElJZmqyXFzkyBgs7lzkMQ8M1rJIRtTwzllcsACf+Ankju8AkxJo0TrJ1doGY7KuovLqiU+PDwWy/o6O/dLmfuH2KDBTyNoi7pFYr7WNW3jt4F4dGt+BzyC2yF1DmR/K5UHwz+GvxD+0j6SCPkQm7ccs4+znjXNfaW13jxisYbXpPGLTPt+QrjB/hd/JvrXOqLyZX0bFnn3utwisBH9ZS2VS63FimiQQdaYTk7xMaruYzDZzx4nNrtUxA9+5Zem33pIIuXWfP0qEQYS2069ETA1c1Tng0P1dD5wIzEoUum11+k4RvUdwBAv0UQT/FZ0K4qEBcnyx4+NeHzXBu85O1UVH+1amBrMR7ug/BksNYiZQbToWZIxr6zxx8+QS7de7CwAbFX5gDCYXOjLJNfOJPr1ue4eOjs+sYl7VdZdz2L7q7fSWCLHJoK/or2nCSg9Lqu6DPuvMSIAo+LLEslqWwf7A/9t2gEnHr+CLdUX00eCAWNNpz4jt+kXj746dUSbJ9ND4YOTtbgKL4sK4W7o5ARxqiJuC1YFYbx3nqpq/u1eH5B+17PUFm/o/bDfxG9pMcpXtO/PdRHulDAfh5qNpjmI87CewprGf2PwtAmtS3tuyqLUv4EEbkMlnORwcXAK1kGZnIq9F7e6bgV2M+Hg8rqNJa2OmyXG3s6edkMxpuO1YZP5i9yFQ2ielw+H63cBJ50CS2kYCgToQj3DL7x50OllxyTS00tuOQEae5btxbab9PruVxm4XF2r1S9RtwYntSHhx12CjP4cJEdngic52FCkILDKyA+JadyFE9r6L59r/OxcI0nHwNcGwx5AldvgfipGLIfdPLpjcE485+Oj4sCr1XvKXGv5oAitZ+pXlK/GieXsGFj7U9bOAX/3w2sRbfcIF/apVDyqA+f15MfkgwV/WzI8R2JBjf2rAPNyyTw74h8vPBokAETAIPGiJkemBm9+EQP8ux1jLvfX8ViPR9M/x6B0IPJUw3yHnm1T9PQL7JsBTDCJABIgAESACRIAIEIF9CJDA7sONtYgAESACRIAIEAEiQARehAAJ7IuAZ7dEgAgQASJABIgAESAC+xAggd2HG2sRASJABIgAESACRIAIvAgBEtgXAc9uiQARIAJEgAgQASJABPYhQAK7DzfWIgJEgAgQASJABIgAEXgRAiSwLwKe3RIBIkAEiAARIAJEgAjsQ4AEdh9urEUEvhOB8B5CvBb8O1WkVkSACHwZAoxbX2bQOXXelMCmL2bM6aDf/50snr4oc/nsDxrMK6v4xJdPb8N2uptXFUyB63WUS77KZr4c0/viUIPPO9oBX4L5W/0cafClQqekD+yB36JMvRPr1Eefv7/NFhhHq3LKp6fVN17noatyHlpgjx8cKsBjG5vy68eKcEzrjFsRxz3++i5x6xhP+ORW3pLAxs8r/i1/3U8WGsj103xz3yvO3xD/jc+1KZad7z/LZyE/d2rNhOtv57fFjSdt3Lwt8lnK8pvZ+Ba7fI9+BdXOd8E3CnFw8Yxnf+jhE7Qlyd3lZxi7p9deTKrsfaUzzpD5bxBvbtflfIIv2N8Jv8g9feSWYsl486b2Y9yyw3yXvyIGvDhuvamDPVWsnyGw8fvqdjL5PQJ7Op2WkzuxfiYW+C44SKQNTI8dRZnE/f3Jt+Evy+V6XS7n83IyE/dQngcQ2Fv4Vv1l6X2pfh2TdQILzE+XkqDbiWCLn/XaW5f1uBIq+9BgqT9MXl0CmzEU3zhfrsv1cikI7Uw3x2n33JYUy7+/ZYsfPFfKfb3BV58fb/bJ29Zi3PqmuNXa9/eOfD2BlYwrAo78ZgL3maRtq4vqhNLMmrflejEZxOb81p6eXT4HY5kog42fpkPs+3TxsteS4cCFUuljYakBeF8gQiaLd5NlCDi5A0slVmWf21rK5MuFctCH6txUXPMz2NFgsU3ou0v3ZXeaVgx8ebUtJzuj555+t8DR40GHVMfNfvAggQ5rFn4aiflz481RSjBu1Rf3+/0V/uDHgaMsxnbGCHw/gQVJO52XixAEJbT3TPRjUN/pbH+ARin1vDPhvpMejSxKJM7L9ek2lTVQjUT5gMpmgxsC3t/yd5LMnGRrT8vZZm3vsYH2eY9fjwksfKXOYojiONdb9qPnPR1hv4b0ZEgfuaWyzfSvOFvbQroxfovWLZdfoPY3/K5hqec9P3hnANR2r4g3RwHDuFUjqf7YGft63vPXF8etWpdf3P9+AisPUVi2AafblAW5few6UR2AnQGqt8W8AfrGI6LUK5NDj1ztVUOy9+fqVvlcWx0iEx7quVRLDYTExiUI1k3rfvDgkPy6f3aCdQu0B7VNPdWRO5zHOZ8gl/bQBnVj7Gdo2yOF2sTDNtZkLzpWnB1ZV2NL9tMe0Y99Md4UmL/BTukj2Y4z8UaWr4XkyRvoMRYB47C6wGLcWv7c+RF4ObFgDDTPHoTA1xPYBqfVSaaqoeWrQV0V27Srk6BPBqSt8YQ/31sZeNt6a+fbGtWRJ+qSe0bgyDY5Ci/pw66XnpmgslzYgnydwJYwi0sfOmVCU7fl0nlQDHKp3mbtrV0y0163+G3KOt7bArkzrtBI71y0DYYia340ex56ab9P2FiTrRBB/b2120w7ai93QgypbF3y1IG6EGdqR2VmvJnCqynUjotVO5o2ctnzcs8qIdPkgzahZ+vboUPGrQZ3jPlXxK1GmB88QAK7YnQNPrJ+dlc2zungXSYUJeedgOWI3hx6oi7at8ptJmSV4x5dyqfHd7+hwZMvC7+chWwGApMmDJfMYDKR9bTyoNg5LDc4p/W+8EXrn5a4YrskQbZNkSG2qevC5SG/RITLenmJQH0caiGQu5lFxWNgG5TpdYCOHvA7lL3ur+tnc1m5bC/ju6aPfJ7xxsCSNxV/Hz8pqBi64yo3Nb0F37R37VSOgU+jg/BwZX7eQC4WdxFZvMJr6hedb/j19NTqNlbZbS2QNmyMYdyq0eH+sQi8PYHV25y9QXu9pEl3IpAIdsNB6oEbXzsSM1Te+R3HNPg9Pgjr5Hy6mHdSylPRCKjyap8dOqDKE3VBl6pTIXgmEC6JQmXv96gJJrSdAzhIpu0Ssqvo8Ec9EEvrJGwnTW3IWcu2ageDj7RZr0TQ+vEBtFIc1O2PMeglxDy/+3SDn2n//TGh6h+8obLLK+V6cQbHu/EGGK0QT9jbtasoxngzNO+En+jYOYjAWv/IsmV7T8eb8Ho1xN2/ZdsFco4ruDgd/m7WPbfPuPUZcSv74u9uvTeB7dwW9Qduf3ItzLs6gRSlH7PzxCCswdfFUtZfyqR9h5pP1CVIqf219taJq0sOaj0TWQA2J4fY1VVG+/b9n9KWV1bKFOxQbum3/ardirJeg+mY4tLrd+JCT8dGvYQAk1unbfsQF7Asfmf8DH20dh1ofcgpxbqQGW+S6P3WckL+GrtKRMW4j2VV4/7dNd84MGs5xnLGD1bUfaIuQRLtr7a3yfROx5uom12ihFetrYfgGCfkoc+pf/cNKR1sGbd02U7JLWb8FeO+9Y8O2jx8IAJvT2DjuwTl/aW9f0wwkw70igmkNpgGxf4kpmRs85V02ZlOKPLkuw1+moGN+HlX3WVLnb0n6iISDHFRWVZIxCJfoTHvbMUbKjoqzhyu23PJ60xDqYzq2X3faNWY6u77lLY39CcE4wo/tD2oe7+fIaM1OY4r9e/ZVdn13aW9WGPfo1zL2cGuFuwV8Qf2GxCtOf+olWn3FUvGmxac6khDZJvbIlWFB+wybiX+sNtfXxe3HuAOH9fkexPYmeyTBud6QunY4hUTSC2KyuyTDSl++ITiYhkzkLjqLIqojLhAML+2oJZ7vC5ye/WSPsTQI9x5Au1/3UmxFcJidantNLVfYrjttuCog0yIxD6nkB0e5GlW7KC4DPXNfRbF0PYMgS0qQr8SI7eIsa1/Hm0d/zuHTeoXWDQXFuu+GVp4RfxRmR8/RsdYDvxAZTRxBhlx6xBa7vG6HBVvxh5bYtKLa+M29pyt+j3si4w5hjBu7bEL62xBgAR2C1pHlX1iEB5PKKJQnniLtVxhXWjndpV9mO2JuuT1y84kh8lOf0cXNDF444EleZhp32tuDHbyTtejMyjV2txwoSGZAq+foR2ynOMJMk8+ljPo+0t3E9iBn+mYyjIWfev5x22sjxHTt+Jc+1eWf4SxXjwNsDS9HbOpMj+e9K1jmXH6nXjjmbG6C5Tix+AS1Wtk5zFjA8atlY/gGKzcwJTPu6d3WojV5hAggZ3D6dhSbzWh5CfM/Xfdraj+Cl2UpI6J7IhIRK1qItshhy4E5o0F966ddds3B+U9jOf8hoCQ2bAXEVJ0aIccZMeYPJLArvkZZKyJocHhQZvrpMt0rDi3cs60owT2mbOdyvwOBHbNDwzW3uYrdDks3ohC8mU6s3xpmrhKvBktbanOhdfieQAybllUZsaslnEvOl8Xt6wev7pNAvsKy2sQbidBiDMeNCi1/qvtDCZMLeMO0JU+nqZLJldjErZngqwJYiSyo2zIXZitQNo/jWApxL0iI2qH6nhqTOUd+EEmwdUaWH0/rN+2dDHTvpZx/Qy69cdEH5f7zqhcI2zQheLcyqnk1NVPGoCOK28qQF9H/Q5kRheKQVd2lBz/ajsDLLXMnr6epsvR8WYvcQXeWZ5wJ2aNVHewvQt7iLL5N/s949Zm8FhhgAAJ7ACcx53KwciP8/n8rqyoEVwDlt+RydztnVSzrH4X+fxduujawZY4GHXjppatiVhTsjrgTzJVIYNZn9A1dY46oLpVfevEXh1P/Sq5atZuZsFymRo3TEB97O/3M/iJL3+W8vitVdltl4qzg4Weq/FLDeh5p67t4/BtYNuRSy9Q8H7i/QKsYqkY/E68kQelMulcvzjej/5KTcX++WMsL/+q+l6RKcek/pjJZWr//u64tWLtnzhNArtq5khqwuumVsvOFsDA8iYMyQaaW+OdK+nZnrSthl3Wa7CqwDLbgckqtQT1KF0MXo0enqBby9dtZCLrZXs1YN5pm7pXu3+9+C871767Gdg6iKPVTGJaO8nXx+wk27YBP+rBj/PFusbQ9aSfof8hptChP5lB2y2/fdmdVnTC9WXQtmr72HHSAzHhJbeYGW8c7BM+eJCz9eP3jDdxzL6QuCYoNXYMx1gP97njjFtzOLHUMQiQwK7gqIP+yC9xSZ+YsMOtoPzFkvhg0Xm5XNILr+8MNnlCNaS4uf3kT8Yr0OTTj9ZFSUNLrLIQ5Va2215iLu05Hwywt8sbHB2Md9pP7Za+lhVegWZefdYSa0Pa9ctdMmkaXAo7yRsYyi9xnS6X+JWwvxZnxbNoMLet8g4x6fsZ2m/1yn3omNmJqWmp2FTZO7oVhdUXe7qAZIsvYFyb9cu99wOnToCDu865EGTjTmF7yIW1mIw3BZpq43YcFOXMTrabE2/kIxim7Ks21c+HYzTFsJ1jTPtg3HqVmX+qXxLYNXObwD8zv601Z8/fisX8CBzxpfYaEHcGEvSjAcULWvJE+5YXXqNR5/eRuigWTVbLEQSHzCQ0JEUov+F3iGmN8077ZZ0rUnw69d+YYHTGLcvaZ4v3Pqqs4gcyxWbyVdfL55wJeo3Ur/oZ+u2RwmgcYPIwe7ZKt16hGA9ktS+GV4zlgqH/ajftiPFGoRht/FK8GeGw5RzjVovWEJOD4lbbK48chcBbEtijlDuuHT8Td1T7+fOVR7X4una+SZfXoZh7znjOZ3G0Tm6m3cKnUTd8hg3B/mgCqZnVFQIZ+x8Qx1bLFx+RuJH+N0nCeDMLl+L7DinOWaF/oFy2C+PWD5j7ZSqSwL4MenZMBD4MAc0++lnYfdpg6cMaMU1Z2p0Z7X2ysRYRIAIfj8BL49bHo/fWCpDAvrV5KBwReC8Ejr6NP91emoQOz/6+F7yUhggQgQcgMB1nJvs+ur3JblmsQoAEtgKEu0SACIwQQMZ0/gGXbmvIjMxkVeVjDtfrsmHFQ7dbniACRODXEHhR3Po1mJ+sLwnskwHf3528jugaJnGZyMf/774g7Jt02W/RT64Z1rjdrUBcH3p3M2zgAQh80xj9Jl0eYOofapJx67uMTQL7MfbEk9rVU+nmKWc8ed6+H/HdlPwmXd4NW8pDBI5A4JvG6DfpcoRt2QYR+A4ESGC/w47UgggQASJABIgAESACP4MACezPmJqKEgEiQASIABEgAkTgOxAggf0OO1ILIkAEiAARIAJEgAj8DAIksD9jaipKBIgAESACRIAIEIHvQIAE9jvsSC2IABEgAkSACBABIvAzCJDA/oypqSgRIAJEgAgQASJABL4DARLY77AjtSACRIAIEAEiQASIwM8gQAL7M6amokSACBABIkAEiAAR+A4ESGC/w47UgggQASJABIgAESACP4MACezPmJqKEgEiQASIABEgAkTgOxAggf0OO1ILIkAEiAARIAJEgAj8DAIksD9jaipKBIgAESACRIAIEIHvQIAE9jvsSC2IABEgAkSACBABIvAzCJDA/oypqSgRIAJEgAgQASJABL4DARLY77AjtSACRIAIEAEiQASIwM8gQAL7M6amokSACBABIkAEiAAR+A4ESGC/w47UgggQASJABIgAESACP4MACezPmJqKEgEiQASIABEgAkTgOxAggf0OO1ILIkAEiAARIAJEgAj8DAIksD9jaipKBIgAESACRIAIEIHvQIAE9jvsSC2IABEgAkSACBABIvAzCJDA/oypqSgRIAJEgAgQASJABL4DARLY77AjtSACRIAIEAEiQASIwM8gQAL7M6amokSACBABIkAEiAAR+A4ESGC/w47UgggQASJABIgAESACP4MACezPmJqKEgEiQASIABEgAkTgOxAggf0OO1ILIkAEiAARIAJEgAj8DAIksD9jaipKBIgAESACRIAIEIHvQIAE9jvsSC2IABEgAkSACBABIvAzCJDA/oypqSgRIAJEgAgQASJABL4DARLY77AjtSACRIAIEAEiQASIwM8gQAL7M6amokSACBABIkAEiAAR+A4ESGC/w47UgggQASJABIgAESACP4MACezPmJqKEgEiQASIABEgAkTgOxAggf0OO1ILIkAEiAARIAJEgAj8DAIksD9jaipKBIgAESACRIAIEIHvQIAE1rXjbbmcT8vpdF6u7vk3P3i7RvkvtycJel0up4TXhi6vl9NyvlyXDVU26nNdzqf1Pq7J1ofCdZO+/5bTnY3erpflenMQul2W09/f8nd+gIdez8vfo9oOFrwuZ2n/7zHj63Y9B2zuheZ6/lv+Tqdl1YRii5lyG723Xzz69el8eeDY6feOM48fv+jp0b/JH089PG/L5bTNXx8SUyZhuF1OYfze6/+T3bEYEXgZAr9LYBMB8AnGOGDFCXJiYnuVWUFu/jbKeLst1+u18++QqKQfAubfpv76JOZ2OS/n8+T/iF1MEbG+HHeZD31vwqTuEbI5doSNHzFLQfZHtB1UhF6PIbALsLmLII9jQGGpQ/orWlzZSfh5hOt2CRdtQqi9/2jSRIA7Zep6vhv0bXjE+A0XD+EiR4jjzn9fcAfbAZ6h9AZfSK1H+Z1xi7E1qdO0Clarp/uj7ZzbROB5CPwwgY0ZshAcm4mgH7AsWTtf+6TueSb0e1I5G9388uHoKLh228FEliaZbrmyX8jnXUBsmrwGER7tDIosC3QeFipln91D/3+TmDTtQjavPiapB8htMbndbsvMfyP78AB8ZiOBDXcW5i5sTiFjJhnUmfKS5a4E3ogv/HmcEb8tt+4FYr5wrEWpJFuWZUC4IPdfRWATYYruYglsCNaNbwAAIABJREFUJoc1cQ0Z/r+/xXMx6Puo8ZvHTqXHFOlOOtWCYzxNksctxLntSmToE1i5uze8SD+1WVS5MGhs1MFDZe+cr9s5jxIBrQPyCBF4CwTeksAiOOogvCPgeAE2I39b5FZP7OdsJjGPwOJYnBSbCS83+sCt23Kdzk5GvU4zmUwTvFqykibLOkInLTHRCJmH3caYS8UxgYltij0G5Om6cgsdE7lH/oyFVP7LoC9TXjeH2epERmTC+YtLGPqZ7Vi2XSWQ/U1uFTf1Q9vii865giSt0yHVCRubJ3pnokZb7u/Y/m4VOQib3hEP/JiS5Vf/v8RlFDKx67FkJJ+ExmUEsiSmsdX1usSq0DuTxlaeLEsXB4wfz7cTRs0YTDZthjEwbU4I3C2JijJBD/8C5IjxG9uYwcJDKclX6yTZaTcenuJyHBmr7vm4JEUIaS+emhAaBOrK37NDrYZTbguBrQnq2j4JbG0A7n8CAj9OYKOJYqC2wRLkIQdoWTYgk83p/Mg1m2suA7lGE+COc0WgT1kiZVSdySDwiUT+tX6WTw85KnkTYwj4aR2hToBOXT3UmXhj3TEGKhvaWCNEWkF7z5nbtbqT55sukr+1BGesW1PeIzlGDXcTfa+S40zWMk3G+vFR5szosJYhqtZ5WjLZ244XpaflIhdVo4sgcy7gAL0HNpMLtbge0ugwKA97RPuOM7CxXRuHXOvkC0DPtlsJLOJazcB0fLfyPHL8QuMuAUSB4W8/ZvnVUnngeUsXlVoYNs/zgZ6yG6meXMDAlvaCJowRxTuPHe+CR9YXi+80ccH2x20i8OMIvCWBfYVNlK+Fzv2AJZPha/8g17bJuTuJe1nMegKs9wGATvZ1UE+TgXf7LNStJgs5hrbSBHIEgXUzJem2MiYFTMTd23npNp57W1hlPi+XIuO5MjF1ypauBTvLQ2Cd9p6RgQVQsPnUb5Yd5O2uX5AK7VvuQvQetml9Sat5G7IkobqVEsfKJT5kJuTZkFwd/9Wxuoy373VfHgNuMp7WLgIyedbMGmy1Ml5RLPaNPluSKud9EvnY8QtM9EJ07QLHPZ/wKZVF0/5vsGk81SY0hM3LxVBVtTqAeOL7e8IYcWPiomeNwN6Vkd2CTaU2d4nAuyDwYwQWATtPAH6w2Xi+mWSteW8HPikM+e2Ecw23vap5OAmAifDsP0mdJruCoNUTYL0vLaNej6Sa83WcbCdF6JSzDfcTWItPtgUmmCgTiHZNwHN5Jda1ElIEE9HQ9qatDZuQc7h2Fhh7sm3oyy0K3R7RduhwAntXsGXBnRB3fSEwKWwCwmWXCJU+3KiZ9Jfj8YGkHmEW3z0t5Vr4uCypaRP6hHW8XnuQU87lMTEdn9BhwmBmCYH6WagbLww0G4gLpOpBuEePX8D0WAK7shQrXeh6F8FIVAO7Euec8VeczF2A6PppaYo57l3wwM9hVuBifyFDWNrgEnnvLsgOcm875TYReCMEfo7Arq0hxYMLceLor3kq1kr1XgUFInDYrSAE3vzQSQ5isrwhH48+honQJ3QLHopBVJZKZvIObVT78Q0MEgQ7bcK5QSZk2QXwAR7yejJkItNaQ0uilcCOMl1e9ribNUpomNtywK2cgCB8+oW83iyCcwVZqurv2VXcJvH1ZJvoNxKzzoMkyDwLOeusCYzHPSI20TnWcFbkaKamlMHkbn1Q/VKWPajf5Ac1s51lDKWlL7Lm0bnyU/9Tf/IvcuBD1nftxZ1nGtTJ8iStYXevUgOMJbvVSRDYet208f2AoWIA3RAr7MW74GPaV59/3PhFb0oA66wnCgx/Ez6F8LYCLuw9gof1sPEVaprhTgTxfM0+JQ8IOu4TOurKnzDsigYxJ8rBl1bbQpvyu8nPbEVuE4H3Q+DHCOzIADGoCXEVwoU1TPI0c0sMR+3kcwgwsc1dkTg3NtpK7xxFtiav08WktEKGbNt14DT7+YG3OPG7mQMlD7LeLz1oldYOgxxDzvxbyheDv51IB9tV9O5OHCF2p3VlF8iFydsCYLaT7gVBwWmcO5rABoJ2Ce/HRVfu750T0SaMu7c7V/BzBZeDiWDsJLCh2fSuV/H13J7vJwVJVbv1yEdJfiJOjp7A39NBz1UEMAjeGZNJrobYuhiuE9g8tkpMBK5s+3LcLZL7xYWlZAjrvoFd4w9lO7n9sm9Xpmr8osvYRtkuzq3/ljZcL1+WiHG77jsmD5Dg0IvysqrudeVXDDvkGZnUhHEHntAP5hfx79VYjLiMmDxqWLXgBhF4bwRIYBcbmBC08iRzlpfcI2Cn24VNYO/aON5OFAI8X6fb2OoJzUJpcIIezgTcaa0O3sV+CL6CEdpdmaCE3AVybfoPgTR2jgBcT9oa/HUyddaB4han6hrb1LoO4OgvVJEHLqTM7bJcbJbJ4oLJpuojFMG5IwmskDJMYKu/GfuZOvVTxhGnvGzDqr2+fS8Bvbd+ktCsQRQ/y5N4WsPau0sgPthTMtkVJo84Gf8N9bL/o1zTXCLYNkusZUBwje+0fpuWIti7I9rAOoENBAukRX4LveKyo0tvfXU17gzMxVpQjKcjxy9UhH/KhyRm/Lssk8ZG1zjoxf8tYh4uKM1r2XpZV9tatmfE/gRbJzt0193jjofzGi3bvmwDf/fCAHNW73cnNrUM3CcCr0TghwmsJa51lhUTVJ64JJsoX1ZCsNiblT3M2AiE8laEYja2k/N2otAE73CrEcQ+S58zNQ651AmwECxXli1nEkcBnzTgbPpF/SoQ54mjKm8Cfq4CfFr9Qm1g7JGIdG64TrUVYXwEbfYmnTuO+yTjWAI7/1BJHkezBKUm4BHINIbtBSL8Ard36y+iyfmTPHjn+2bte/W+9BuPjb6yFh/4AWn0SKySj+CMHiEd+aZXPrlW0r+2N+5+qO8Dpwmf0jrWe1EfxMyc8zAzp+Mm6ruNZ4xn/WOKwL5gfGG+0K/OpdfvlTG7QSdcKMgyq1E5+BAzsA5+PPQTCPwcgY1EFGvg4jtd28kMa6QygVVvCOtG1+pr6YdttITaC3aYBB09OpJhcs6BN5ONZlJMbUj2q8UwxOBOL7hA8InjPRMg5PcewMAFSDFn6qTmYJTOuXqjXtFYR903PAyc9onv+xUmVM937j1W26Dw/0RW0X95xwO+Fsm63qUIy1rqNeMghnmNJ5YS5TdNpOUn4RVjkjF37q6o31xDlswtYx7UOqd14I2OWKfaGAlyOn1vJLB1n9ZVgWfTvcp+/PhF/96nWCXOBFKHQvKL9zEX1yPpQw214CirF9idi2/c3Qnkfu49zvl6qEyMyMULPped7xBsuOWfsuhWZW4TASIQEfgxAouJt0dc4RZYC2azmTiHXxuo/ECOko/8tROyXuWjQ2Q5vEkWZapf/+GeSNgx2ZWEFQShJoD9SRYTI9qrREgZrrq9qhR0qyYpELMRYaqqaEatyaYqESlmxygICezS+Ftlov4uxuGKjZ0GxPdwIRLIQVj/Z++OmAfPcPtZs4zoz37ARAhGsi98Ssvnizf4U/DZtAQh+lo79uGDtZ816hT9te3ImtRIoOtMeX9s4c5GM7aSv6pMqe+mnBES41TrpHM43qsb9QfWpkG7Cd3rxkOZm/twlIv3YIyKrzgj10pRbEffQnJCHuDdWB8XHOo/xqaIF3qu9S34mPerMAG3ne0M2y7Q4A4ReH8EfozAyhW7l6msDTWYIOqisoY2X343Z59zIJJpnYjRKYKmRj+c2PhbTHaYVPMEFSc0E6yl+U7fmPzkCd5L+qpYuP0XHp6L0809E6A7ySV10XcLB3QqbwujvDdR45z7gNdGeP3i4ledDNHs8cHsHXGKDyxu72fyIThfMfPQVfahblF7wkzeBbkwx2WCtreT81sUEjExF3OSxY3r27Pv1lky9UWsJ7XyuD6+JXbYW+VONlX6Qh/Fw2KDPoqxaoRN7ajv98qZKvBxrWOW4Txq/IYH8sJSrdY33LGd9GrHaMKowM0op5tYo2oIZYhN62Ovvr0f8YoZ18tZ2st+Jd3VvqX78MOwHMzPzmZx7R2AdRlHY/uSvkJp7av9cIMIfAACP0ZgZWlA59VBxXFMdiabU5yv2+hMPoc7wDZSgwAV1uuukJ46GBeiV5NdM7E5k4g72Zj1g0UmIGTK8rpEkKuiTC/jUEXfXr+iTyO3VVJJUJ50UL6dHDPx8M7ZZndvqzxmYu1h0Dk+km0Txp32uxlYyG7IYonDOrmAfJV5l9ulvu1fthz3/CVA8gGE9lrz5i5/QatRjpZMaT+BbM35DNq0v9BTfL3WtdeHvnXBwxfYd2ymfaRyo9iA+KF1njB+g84g7ZV+EauMtS1b+zpwrY8D+2YpWQevUQyyuEi7NuPryiqF0oOaRV3YrDgISavfLWWrqvUu4ttMt3Vd7hOBd0DgxwgsJs79pMAPaL0J7mATI3jtCLa+3BkHDWLhieVrIPryCrGQRUgZAp0MIIdWqjNC9X7GQYJ8WMeWbsPmM3kLwd9dx6oXEukiQ2WI9VEXd4VzqysENhDc8tVKCPCqtzaWM7ZV91ri7g2DsWZqkAVc+3UuKGp5MMFvegBE+8U46vg9ZK8ISJZhpb4hSvvwhX068mVBVrciToN2LNmC3qtZv9St1sVt604/zVjpjy8sIZAMac4+n5dz/VS7yppjQC9GWBs8evzCIPBPO/bcse35uuJaJha6pLXrp5Cm/EVcsLiUJXCBW5Ht3kU0bNHLwNrGTVk9jGMT84KVeUYP7YMbROANEfgxAjtjAUx+KbBvDG4zPewvM5+Bxdo5Wdc5uo2Ec0KStA4CYXiRvdSPt61y8ENZTLjVvjepbFB6lTRIWwjaWajQgzvJpb63Bux+eRCwdoLaoOa4aEe/caV0dgr/eKtyqj2vUCCz3gljm+7YAX7wn7YdEBhr3vm3HIAQ+i+jt0sMsG2X38QLhnihhTERy0lMaGWGrCCAVuZWMxwBBtGHtI2pymMCK2TV6hN6vF0CodULO9n3ykG8dEEnek+JZOpFXVqcTJHu+M1lSnzkeGy3GnONr7f1tE0ltuk91lhj3PVTrVls9ONCLubK2tMBYx1xt/q1JN6Ne6n+KJuOj3dYW87okTXiFhF4PwRIYCubYFDL2sZiuyo3t5vWpm58GGCu7X4plVsC4eCVQXULUi8GwWrxZAr8o+AX+kxPg/eCd90f9kNWJ6yHjQ9N3DMBjvoGLlYPyOD9xracW7uYCB0y47Wz6xgmtVlhbSfNpG5Pyna8xR6yr+kUHgYsu6suTLQZ+dDHaWkeesN5yN4lBiAZfZLjYQ/7gSge+SskAX267aZlLmf7yq5a3zDeyqwfipS/wPVvyWuogYnjb2VloUHLediX3EFpl0sIMW//ZA1oezz4Q+kMbdV05MjxaztReyc/csd24esZ14L02UaL7VzetXlFJOsyI3hcWWG3am2sktJessGaB2PLdg4Cq1cnhZJxZyKGO7V4iAi8NQLvRWBTlqC49aW3jKtbYpuOt8Hcs4oGTENMdFILn6j0avWP5fbKh4P6Ne48U7ziS9bvmkyUeZ3L5l6c4BfWcjmT5NrkKpOoZHTDByLMe3XD5FBMVH1yE+T3Ankvw5EUhj1s7B9hAduX5fOkNzdJjnoYnOvoN6iRTxWTej6sW+l8QUBxrFRWL+JKXVcwgOwHE1iVf3UD8q34UNWOkDaJPfEF/zFDHX1g1A76yrfiiwfMqj5kV79oV+MDG5j441RfJ7CO/X1ChaxmTZqzTpU7hAeRHjl+S33jMwvg164Ota7ylgrvIqNsOO1Bz9lnHdIclOJWjY3tYiRrJMLGpzBeRg2ica8sjtXLRuwcWS8hCRn2OD/MdIvu+UsE3gmB9yKwGsDzZFBf9e7br2471RaoiF95IVu9csf7xGLdHvaNPg8NEkIKLVmVrKtetcdz+jUx9/2XELjzm/SY0qGeUGyTCLSa2ZCv7CTCYLJD66TB3KauhIp1x/5TVbESmu08uWUsA/tIH7NY8SnT0q5NYDUnbNnFyAa9LFDvOOSoyRaOe2QL5+o6KiWyjWYS13NxA3bco35+/VS//aq77u7IF5G11osv6B38O96mrhvGRVT9hDrKSX9yF0SHL04Uv6MMbMdvIVsNKI7XtsJxa189hvF1/Pgt1Kx2oi2qcTf09aqBZjdhVevelCsPwIY1lLZUK6uxC946IJlYYefAddQgGvfK4tjf+lfLbBczeqBb/hKBd0TgvQjs7IumV56ox7pO++tOCAVxjbfbcbVfGyusv7PEK2Qf3VarqpLJqQ4dsStYyQu3iyxmfml224V9b22cgIQ8XleFM4E34DXOhEOe8gEsZMBFBvl0a/t+Xbu+US9S8B5P9xeTaHptUorMceLorH1M9rNBXF6rFv2kfH1NviCwJAjEy976bZE+5IhOSllPxUX9cHyuzJpGqRSfAoTyXFkP9q+zdDl7l2+DJ82N7FhjWv4auV3b5jsHjpgT8EJma7uJak6RiFfZTvERhXBBaN4XKmOkMyZBGOL7a53OvEMmJmJtbnxFU8cHE6FrbIL1nvXta71r0dpX5VUjPHj8Gl1t7MZ2xDXGOBzD2s7h+k+ZL9wYDD95fAa2wVI/NWzGQu8hLsEFcRpjS22SL+bLces5U3kMscA2VZbgHhF4bwTei8A+GiuZXGStZbqdkgmBny1pxJFAYjOdIBIrD0M07ew80H2KdtPygJbIhge9VCZD0qCf/EqUQ/C0x6e2q6yJ9pU3NMBPtWeCPsqnKByDst8f+igC9opOdlJAfe9BnqzJQVtGrpL8rWdZkG23sgepQG5sVs2Ki/NVRgp6N+2pjBXeetyxE+w1+VvYyso63AYxKYnnsErnZEFgNXOW9BqsLy+ys3hFVsBl40NRAyxbbKB3ZQ/oBvvWFdFHZXddDuSQXjSJX/hIjqkbbS8yQb5J39jSV+O7QXDgtVHWJF8LY77wirJF/xNfsPvALHxF7HxaMF5H+mhfsJUe0NZWNjpxvRcLVlrjaSLwDgj8FoHV26QSsNIDS7iy3WQNefAhPsXrBqZNbW0pbIOQZCKQ2dzSBsoaIlsEw3g8rkMWjM76KUTUfOdfucAIyxKcjEuwmaxxLM7V7wZOOncy7OFLZdcnILB7osrLHNpJO16AFeYuVJH1yQU4xVlvRzJg8jDY0X/3ZYdATA4msMhWDohrjUNYV1s6XF1kZb/2T7kD0hn36Y6SrMH1/2Rs+x9y8R/wkuxee7fEb/uYozHLXN4NOeSYK17yk4a4u4X1IMh6A3N6xysuOC/JDPFipnNRgVbDWz1wN6j91RG2Oy6IrvXFbx0LIQx/icBnIPBjBPb5AflwN3jyhHK4/GyQCDwDgdFrvjb1/6AlQJtkYGEiQASIABGoEfg9AlsjwH0iQASIABEgAkSACBCBj0KABPajzEVhiQARIAJEgAgQASJABN6KwMp6Uv4RASJABIgAESACRIAIEIERAm/FGElgR6biOSJABIgAESACRIAIEAFBgASWfkAEiAARIAJEgAgQASLwUQiQwH6UuSgsESACRIAIEAEiQASIAAksfYAIEAEiQASIABEgAkTgoxAggf0oc1FYIkAEiAARIAJEgAgQgTclsOlLLJP2wZdaJosvS/hizWXRr5tMV/ySguEl78/9ws6xyHW+1HNsJ/OtFd9wf7VXPWjsvJWO86Y5vCTHzuGQHtIg/fMQGNkIEfgkBN6SwOIzkn/Nt/ocaPFpvYnvdUvt/I3y+z8z6UjzAYfs52g/EwP1j8430+VTmk+hkbfrcj5531F/zOdVZ5xLsTlq7LyhjjM4PKYMx85jcL2jVfrnHeCxKhH4bAR+hsDerpeKbHwmebvX3fAdb3llmfzP8Jx7+zy6vpK0v78lfnfcI5GPtq8lM6flfLku10vpY6/AVrGZ6Xz14u89dTzan2bb49iZRepZ5eifz0Ka/RCBd0Tg6wmsZFxB1uT3pBmzRxOcdzT3bbkk/YX4BVxmiM6bqdInabflekl6CUF/oG4qw6ldiqLn/p7vY9r3jO4rBFbbejMdX+OOHDuvwb3fK/2zjw3PEIFfQOD7CSwIzem8XK63ZVFC+3xy8XKHUsJyXq4fjINOXB2Spucd4nWMDXLmxxVBcX5+hlt1dwWrtFc5T8ulWXPxvjpWWjxnV7Hi2HkO4Gu90D/XEOJ5IvDtCHw/gb1el+vNzM67iNuzHnjKDyc9wvFKcmMySi17ObD743Uq9WhF1Vu9HQIry0nCxUxbde7Iqg9lbB+ZBfaEXcOmqKOkzCGwh+nIsVNgvmnn/cbOrPhy5+v8yLhymH/OasRyRIAIvBsCX09gG8BXA19VQ8sfmU2rsgedBxGOfRip6lMeaNPsdHsbvEJhYrdq/4E6rZG0tfNZ7/MiSfmtf2vtS3u5jyOwnZdwRjZtbUBgZ9pZ1ZFjR6Eeb3zO2BnrIQ/J5nXgpwcS2EP8c00ZnicCROCtESCBXTGPTtKyfvawgGwnrLx9Op+X8/m8nOzT9Z0s4orY7WklE2bpxIDAtA2sHcl6nK95+xE6DScv1dPJKkKF8Bq1vFb2dL5sILI5uzryh+w3Bm/0/8DfITZ1v137H6NjxoBjp4a+3M/j5e3HTil43qsuWFcvvvE6sqnf3E3cOsY/61a5TwSIwGch8PYEFu947f5eL4nwDQiLtYkSnFlicVuu59MiJGdHss72bLbzhBUepHJIqp38Z5YzmsbdTZ/Y5Ing/lvdz9NJdTldlqssEQn/kvkBKZXXWLkwlAfDpIs6f8vqpBtqZ8xGBPZVa60VG3mV2Bo56I6do3Tk2Ckdrrf3gWMHquy6GKz0tRfs3nYTH4/yTyjBXyJABD4RgfcmsF4w6x57FIF9hFltAO8TaSUjTQDfKFM302Zudd/9xPzzdFJcXF84LedA3uYxsrc9//7iK7H6FytZzyFJ3nyhNC/vqOQYG+91Y3KsHjvvrGOW7W/gs4oDx07hLorL3WMnXZygndOW5Ti35ZLuNskdp9X/S/1e5+wD7zgGC8C5QwSIwMMQeHsCG9/zeUrv+/R+MSnXk3AHsxcRi1KaHICfkcXTbK43mSu5vXeN7/N00kn4JGTVTICagY0+McS2NEjYa4isu0A26/mOk6dio+/I9cYMjvXGzjvrmGUb2vegcc6xUw+Um/kYzN/yh7e71MUeup994B3H4ENVZ+NEgAgoAu9NYIfRKemgBOwzCexQxa26qVntxvrtNiU9KwTXvk+3fYfs5KRygE4qrwtezAxBVreIhafZLuu3JGkdz9DkQQSqEW/lwBibqnLXFu+s4/P8bFnWcVC8f2TsKKGXC6Ttg6tywL2763YJLb9oDO7VivWIABHYhgAJ7Da8Dir9xElYgziybaNf5yIgrHEzWU6b8SweanueTkoauhNonuDm1/ZWmSVZSnD1XgGV227JbXYPneg9YpOLHb61jo3p8k4C+xodn+dneR3zaMzg3K+MnXbpwF2vpDPuOL/53mNwXg+WJAJE4B4ESGDvQW933clJWMlnf53smghKaLBWbeV3RMrGfb1Apy6Ble9VJGKxSiDl6132zQ894pq117YH/Su5G5TJLR63NSOb9tYlsAa/gfyv0fEFfrYyZpDt/62xUxPZOG7Ut4Yb1/DA5frysLTUxXmAdsbPX+OfQ8V5kggQgQMRIIE9EMz5pvIkPJr0NACvkrBez3P9SG2dEB7c1/06GVkH5Gpdn+3EFSiv6zCXIUJ7R/6q3gNstL8BgX1fHed8el1+RaGzMdePVFbMf2bsWMgqItu9c2HrZGxB/oe/Dq7r9n3dGLSacpsIEIHHIUAC+zhsBy2bAO4E51jRlJkhI15vmsF1bm/W5bXs3oe5jLyP1MkShh4uSsz894/KV4LyhLmeca2hWkz7rgh6fgL3pvH7DiiZcgWr2h7Jqec6/qDnn63jk/xMfWRCPy3bwaqCvd19kk4HjJ1WdhzxLwhx9vBf9b8O5np+wn6HC8cGiQAReAYCJLCrKMfAHF7NtFp2toCZsNwPJEhWY7C2bqqbnIGYWwe6tXwtxDN0in0qNg1Jq9ex+ksvYvZmB3E1KqsMzaucZnEEXsdOsCpXg40RHpsrk7y2tVtHjh1APf6FL8Qx396VOSIeRAnUpo1/zI2dsR5yNhPZVo/12ltKqC67/XNLbyxLBIjAuyFAArtiEb1V5RLNlcrd03nCktdAxWwgXgl1Kr7E1cwz3TarE0pOOhmKqrjsZl194udUMYeeoFPqLU9cIPne74AYygv+jeT7NrO+8h7V+MUxYzt5L+aoYWTtutnqUeX+OcVmxnHUR3pY3adj9ic/E97XYnQmy8SxM8LJP6f+MVzX2/MHv03/6G253T/I/Kb1aPaFXWNQ2+EGESACn4gACeya1UA0/uaJ4FqTy5IDr/AMuaVdfD5WJpc736+YycMKkbLCKqHZQzgerxNEHU7C8m7Y5sXnqHnwb/X5TCxLmPlqG+xzdJZKsTmEwMpVjTxw014gzOhon+KfEWfOOo/3M9hm9KGERlaOnQaSpxy4xz+fIiA7IQJE4FEIvCWBfZSy+9s9OptQTsKQK3/6E0c+6fcbdZrFX/wj/U9WiUTziEzXZId3F9uuY+ySY2cd+l8eO+vozJXY659zrbMUESAC74cACexLbOJPWC8R5bBOv1Gnw8CpGkpYHbx8oOrkS3e/0c++UacvdT+qRQSIwNsgQAL7ElN844T1jTo9yDnS7eajlw88SNo3a/Yb/ewbdXozt6E4RIAIfB0CJLAvMek3TljfqNODnON2W67X6xMecnmQ/C9t9hv97Bt1eqmTsHMiQAR+AAES2JcYec+EJa+5uQbiI+Rn/P/wx38d1L5RJ0dNHnoxAt/oZ9+o04vdhN0TASLw9QiQwL7ExHsmrFwHT7t3f1+ytjLLN//Eea7T1QWv+3mJTi9xDnY6RCD7zPf42TfqNDQiTxIBIkAE7kbgrQjs3dqwASKNpTUHAAABSUlEQVRABIgAESACRIAIEIGvR4AE9utNTAWJABEgAkSACBABIvBdCJDAfpc9qQ0RIAJEgAgQASJABL4eARLYrzcxFSQCRIAIEAEiQASIwHchQAL7XfakNkSACBABIkAEiAAR+HoESGC/3sRUkAgQASJABIgAESAC34UACex32ZPaEAEiQASIABEgAkTg6xEggf16E1NBIkAEiAARIAJEgAh8FwIksN9lT2pDBIgAESACRIAIEIGvR4AE9utNTAWJABEgAkSACBABIvBdCJDAfpc9qQ0RIAJEgAgQASJABL4eARLYrzcxFSQCRIAIEAEiQASIwHchQAL7XfakNkSACBABIkAEiAAR+HoESGC/3sRUkAgQASJABIgAESAC34UACex32ZPaEAEiQASIABEgAkTg6xEggf16E1NBIkAEiAARIAJEgAh8FwL//ZOoRGsE3p8AAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "ea80bf00",
   "metadata": {},
   "source": [
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
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    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "e8b3929c",
   "metadata": {},
   "source": [
    "均值差公式：![image.png](attachment:image.png)\n",
    "比例差公式：![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4935ce3d",
   "metadata": {},
   "source": [
    "### 确定显著性水平"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "d9b1eec8",
   "metadata": {},
   "outputs": [],
   "source": [
    "#默认\n",
    "alpha = 0.05\n",
    "beta=0.2\n",
    "k=1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08f1013d",
   "metadata": {},
   "source": [
    "### 计算最小样本量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "8d0c0eb7",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>timestamp</th>\n",
       "      <th>group</th>\n",
       "      <th>landing_page</th>\n",
       "      <th>converted</th>\n",
       "      <th>date</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>851104</td>\n",
       "      <td>2017-01-21 22:11:48.556739</td>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>0</td>\n",
       "      <td>2017-01-21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>804228</td>\n",
       "      <td>2017-01-12 08:01:45.159739</td>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>0</td>\n",
       "      <td>2017-01-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>661590</td>\n",
       "      <td>2017-01-11 16:55:06.154213</td>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>0</td>\n",
       "      <td>2017-01-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>853541</td>\n",
       "      <td>2017-01-08 18:28:03.143765</td>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>0</td>\n",
       "      <td>2017-01-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>864975</td>\n",
       "      <td>2017-01-21 01:52:26.210827</td>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>1</td>\n",
       "      <td>2017-01-21</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   user_id                   timestamp      group landing_page  converted  \\\n",
       "0   851104  2017-01-21 22:11:48.556739    control     old_page          0   \n",
       "1   804228  2017-01-12 08:01:45.159739    control     old_page          0   \n",
       "2   661590  2017-01-11 16:55:06.154213  treatment     new_page          0   \n",
       "3   853541  2017-01-08 18:28:03.143765  treatment     new_page          0   \n",
       "4   864975  2017-01-21 01:52:26.210827    control     old_page          1   \n",
       "\n",
       "         date  \n",
       "0  2017-01-21  \n",
       "1  2017-01-12  \n",
       "2  2017-01-11  \n",
       "3  2017-01-08  \n",
       "4  2017-01-21  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "b6f3c412",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1203863045004612"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#一类指标无数据， 使用二类指标计算n，则使用比例差公式\n",
    "#计算原来总体的广告点击率，即对照组\n",
    "p_control=data.converted[(data.group=='control')&(data.landing_page=='old_page')].mean()\n",
    "p_control"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2317476a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.13538630450046119 0.014999999999999986\n"
     ]
    }
   ],
   "source": [
    "#因为H1：p_A多少大于p_B（p_control = p_B），所以至少给一个值如0.015\n",
    "p_test = p_control + 0.015\n",
    "p_cha = p_test-p_control\n",
    "print(p_test,p_cha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "51cb7351",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.11705685305416959 0.10589344218918344\n"
     ]
    }
   ],
   "source": [
    "#计算比例乘积\n",
    "p_A=p_test*(1-p_test)\n",
    "p_B=p_control*(1-p_control)\n",
    "print(p_A,p_B)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db5f0cd9",
   "metadata": {},
   "source": [
    "$求z(1-alpha),z(1-beta)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "2b741d0a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6448536269514722 0.8416212335729143\n"
     ]
    }
   ],
   "source": [
    "z_alpha = stats.norm.ppf(1-alpha)\n",
    "z_beta = stats.norm.ppf(1-beta)\n",
    "print(z_alpha,z_beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fdc78cc",
   "metadata": {},
   "source": [
    "$计算最小样本量$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "0a36c5f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6126.235378834387"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = (p_A+p_B) * np.power(((z_alpha+z_beta)/p_cha),2)\n",
    "n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93b97940",
   "metadata": {},
   "source": [
    "$检验实验样本量是否满足最小n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "d9cf2609",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>group</th>\n",
       "      <th>landing_page</th>\n",
       "      <th>date</th>\n",
       "      <th>user_id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-02</td>\n",
       "      <td>2859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-03</td>\n",
       "      <td>6590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-04</td>\n",
       "      <td>6578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-05</td>\n",
       "      <td>6427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-06</td>\n",
       "      <td>6606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-07</td>\n",
       "      <td>6604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-08</td>\n",
       "      <td>6687</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-09</td>\n",
       "      <td>6628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-10</td>\n",
       "      <td>6654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-11</td>\n",
       "      <td>6688</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-12</td>\n",
       "      <td>6522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-13</td>\n",
       "      <td>6552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-14</td>\n",
       "      <td>6548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-15</td>\n",
       "      <td>6714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-16</td>\n",
       "      <td>6591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-17</td>\n",
       "      <td>6617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-18</td>\n",
       "      <td>6482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-19</td>\n",
       "      <td>6578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-20</td>\n",
       "      <td>6534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-21</td>\n",
       "      <td>6749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-22</td>\n",
       "      <td>6596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-23</td>\n",
       "      <td>6716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>2017-01-24</td>\n",
       "      <td>3754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-02</td>\n",
       "      <td>2853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-03</td>\n",
       "      <td>6618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-04</td>\n",
       "      <td>6541</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-05</td>\n",
       "      <td>6505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-06</td>\n",
       "      <td>6747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-07</td>\n",
       "      <td>6609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-08</td>\n",
       "      <td>6700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-09</td>\n",
       "      <td>6615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-10</td>\n",
       "      <td>6696</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-11</td>\n",
       "      <td>6673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-12</td>\n",
       "      <td>6637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-13</td>\n",
       "      <td>6508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-14</td>\n",
       "      <td>6600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-15</td>\n",
       "      <td>6549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-16</td>\n",
       "      <td>6545</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-17</td>\n",
       "      <td>6538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-18</td>\n",
       "      <td>6603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>63</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-19</td>\n",
       "      <td>6552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-20</td>\n",
       "      <td>6679</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-21</td>\n",
       "      <td>6560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-22</td>\n",
       "      <td>6669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-23</td>\n",
       "      <td>6633</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>2017-01-24</td>\n",
       "      <td>3681</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        group landing_page        date  user_id\n",
       "23    control     old_page  2017-01-02     2859\n",
       "24    control     old_page  2017-01-03     6590\n",
       "25    control     old_page  2017-01-04     6578\n",
       "26    control     old_page  2017-01-05     6427\n",
       "27    control     old_page  2017-01-06     6606\n",
       "28    control     old_page  2017-01-07     6604\n",
       "29    control     old_page  2017-01-08     6687\n",
       "30    control     old_page  2017-01-09     6628\n",
       "31    control     old_page  2017-01-10     6654\n",
       "32    control     old_page  2017-01-11     6688\n",
       "33    control     old_page  2017-01-12     6522\n",
       "34    control     old_page  2017-01-13     6552\n",
       "35    control     old_page  2017-01-14     6548\n",
       "36    control     old_page  2017-01-15     6714\n",
       "37    control     old_page  2017-01-16     6591\n",
       "38    control     old_page  2017-01-17     6617\n",
       "39    control     old_page  2017-01-18     6482\n",
       "40    control     old_page  2017-01-19     6578\n",
       "41    control     old_page  2017-01-20     6534\n",
       "42    control     old_page  2017-01-21     6749\n",
       "43    control     old_page  2017-01-22     6596\n",
       "44    control     old_page  2017-01-23     6716\n",
       "45    control     old_page  2017-01-24     3754\n",
       "46  treatment     new_page  2017-01-02     2853\n",
       "47  treatment     new_page  2017-01-03     6618\n",
       "48  treatment     new_page  2017-01-04     6541\n",
       "49  treatment     new_page  2017-01-05     6505\n",
       "50  treatment     new_page  2017-01-06     6747\n",
       "51  treatment     new_page  2017-01-07     6609\n",
       "52  treatment     new_page  2017-01-08     6700\n",
       "53  treatment     new_page  2017-01-09     6615\n",
       "54  treatment     new_page  2017-01-10     6696\n",
       "55  treatment     new_page  2017-01-11     6673\n",
       "56  treatment     new_page  2017-01-12     6637\n",
       "57  treatment     new_page  2017-01-13     6508\n",
       "58  treatment     new_page  2017-01-14     6600\n",
       "59  treatment     new_page  2017-01-15     6549\n",
       "60  treatment     new_page  2017-01-16     6545\n",
       "61  treatment     new_page  2017-01-17     6538\n",
       "62  treatment     new_page  2017-01-18     6603\n",
       "63  treatment     new_page  2017-01-19     6552\n",
       "64  treatment     new_page  2017-01-20     6679\n",
       "65  treatment     new_page  2017-01-21     6560\n",
       "66  treatment     new_page  2017-01-22     6669\n",
       "67  treatment     new_page  2017-01-23     6633\n",
       "68  treatment     new_page  2017-01-24     3681"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#先看两组各自的样本量\n",
    "data0 = data.groupby(['group','landing_page','date'],as_index=False)['user_id'].count()\n",
    "data0[(data0.group=='control')&(data0.landing_page=='old_page')|(data0.group=='treatment')&(data0.landing_page=='new_page')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "af5b8ec2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>group</th>\n",
       "      <th>landing_page</th>\n",
       "      <th>user_id</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>control</td>\n",
       "      <td>new_page</td>\n",
       "      <td>1928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>145274</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>145311</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>treatment</td>\n",
       "      <td>old_page</td>\n",
       "      <td>1965</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       group landing_page  user_id\n",
       "0    control     new_page     1928\n",
       "1    control     old_page   145274\n",
       "2  treatment     new_page   145311\n",
       "3  treatment     old_page     1965"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.groupby(['group','landing_page'],as_index=False)['user_id'].count()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2765b60",
   "metadata": {},
   "source": [
    "### 统计检验"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "74fea2e2",
   "metadata": {},
   "source": [
    "二类指标： 实验组的广告点击率较对照组提高30% 右侧检验 公式：![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "500d7d10",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>group</th>\n",
       "      <th>landing_page</th>\n",
       "      <th>converted</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>control</td>\n",
       "      <td>new_page</td>\n",
       "      <td>0.103896</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>control</td>\n",
       "      <td>old_page</td>\n",
       "      <td>0.121922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>0.116649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>treatment</td>\n",
       "      <td>old_page</td>\n",
       "      <td>0.113636</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       group landing_page  converted\n",
       "0    control     new_page   0.103896\n",
       "1    control     old_page   0.121922\n",
       "2  treatment     new_page   0.116649\n",
       "3  treatment     old_page   0.113636"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = data[data.date=='2017-01-04'].groupby(['group','landing_page'],as_index=False)['converted'].mean()\n",
    "df  #取某天的数据，看组别、新旧页面的点击率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "ec8bbece",
   "metadata": {},
   "outputs": [],
   "source": [
    "#treatment组的新页面 - control组的旧页面\n",
    "dif_p = df.converted[2]-df.converted[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "a0e81440",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03611589135013836"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#PA-PB=p_cha ,求 pieA - pieB  对照组的广告点击率 * 0.3\n",
    "muzhicha  = data.converted[(data.group=='control') & (data.landing_page=='old_page')].mean()*0.3\n",
    "muzhicha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "27d11220",
   "metadata": {},
   "outputs": [],
   "source": [
    "#求sigma，先求该天各组样本量，方差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "face36e3",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1030418808077592 0.10705669071499838\n"
     ]
    }
   ],
   "source": [
    "var_A= df.converted[2]*(1-df.converted[2])\n",
    "var_B = df.converted[1]*(1-df.converted[1])\n",
    "print(var_A,var_B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "4831de7d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6541 6578\n"
     ]
    }
   ],
   "source": [
    "#求样本量\n",
    "n_A = data.user_id[(data.date=='2017-01-04')&(data.group=='treatment')&(data.landing_page=='new_page')].count()\n",
    "n_B = data.user_id[(data.date=='2017-01-04')&(data.group=='control')&(data.landing_page=='old_page')].count()\n",
    "print(n_A,n_B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "64737317",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0056593454656348454"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigma=np.sqrt(var_A/n_A + var_B/n_B)\n",
    "sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "e771ab8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999998697"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = stats.norm.sf(dif_p,muzhicha,sigma)\n",
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "473d1847",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "显著性大于阈值，则不拒绝原假设，即实验组广告点击率小于对照组\n"
     ]
    }
   ],
   "source": [
    "if P>alpha:\n",
    "    print('显著性大于阈值，则不拒绝原假设，即实验组广告点击率小于对照组')\n",
    "else:\n",
    "    print('显著性小于阈值，则拒绝原假设，即实验组广告点击率显著大于对照组')\n"
   ]
  },
  {
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